Solve (-10k^5)(-k^-2)

$$( - 10 k ^ { 5 } ) ( - k ^ { - 2 } )$$

Evaluate

$$10k^{3}$$

Solution Steps

Multiply -10 and -1 to get 10.

$$10k^{5}k^{-2}$$

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

$$10k^{3}$$

Differentiate w.r.t. k

$$30k^{2}$$

Steps Using Definition of a Derivative

Multiply -10 and -1 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}k}(10k^{5}k^{-2})$$

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}k}(10k^{3})$$

The derivative of ax^{n} is nax^{n-1}.

$$3\times 10k^{3-1}$$

Multiply 3 times 10.

$$30k^{3-1}$$

Subtract 1 from 3.

$$30k^{2}$$